Position an oven rack in the center of the oven and heat the oven to 350F degrees.
Grease a 10- to 12-cup Bundt pan. ( I used a 6-cup Bundt pan and 5 mini 1-cup bundt pans instead)
Sift the flour, baking powder and salt together.
Pour the coconut milk into a small saucepan. (Be sure to stir it well before measuring it.) Add the butter and heat, stirring occasionally, until the milk is hot and butter is melted. Remove from the heat and stir in the zest and lemon juice. Keep the mixture warm until ready to add it to the cake batter.
Place the eggs and sugar in a stand mixer fitted with the whisk attachment. (Or in a large bowl, if using a hand mixer.) Beat the eggs and sugar at medium-high speed until pale, thick and almost doubled in volume, about 3 minutes.
Beat in the vanilla and rum, if you are using it.
Reduce the mixer speed to low and add the flour mixture, scraping down the sides of the bowl as needed and stopping as soon as the flour disappears.
With the mixer on low, add the coconut and mix until it is just blended into the batter. Add the hot milk and butter mixture in a slow steady stream. When the mixture is smooth, stop the mixing and stir gently a couple of times with a rubber spatula to make sure everything has been well blended.
Pour the batter into your prepared pan (or pans) and shake the pan back and forth a few times to even it out.
Bake for 60 to 65 minutes, or until the cake is golden brown and a thin knife inserted deep into the center comes out clean. (My smaller 6-cup Bundt was done in 40 minutes and my mini 1-cup cakes in 30 minutes.)
Remove the cakes from the oven place on wire racks to cool for 10 minutes before unmolding onto the wire rack to cool completely.